We investigate the systematic errors at the second order for a Mueller matrix ellipsometer in the dual rotating compensator configuration. Starting from a general formalism, we derive explicit second- order errors in the Mueller matrix coefficients of a given sample. We present the errors caused by the azimuthal inaccuracy of the optical components and their influences on the measurements. We demonstrate that the methods based on four-zone or two-zone averaging measurement are effective to vanish the errors due to the compensators. For the other elements, it is shown that the systematic errors at the second order can be canceled only for some coefficients of the Mueller matrix. The calibration step for the analyzer and the polarizer is developed. This important step is necessary to avoid the azimuthal inaccuracy in such elements. Numerical simulations and experimental measurements are presented and discussed.
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Second-Order Errors Due to Azimuthal Mispositioning of Element
Error
Special Configuration
Without
Without
Four-zone averaging:
Four-zone averaging:
Table 2
Calculated Elements of Matrix [Eq. (17)] for the First Compensatora
Coefficient
Value
The functions and are null if a two-zone measurement in A is performed independently of the angle . is defined in Eq. (18).
Table 3
Calculated Elements of Matrix [Eq. (17)] for the Second Compensatora
Coefficient
Value
The functions and are null if a two-zone measurement in P is performed independently of the angle . is defined in Eq. (18).
Table 4
Systematic Errors in Mueller Matrix Ellipsometer for Isotropic Sample if and when the Four-Zone Averaging Measurement Method is Performed
Origin
Table 5
Statistical Study of the Influence of Element Mispositioning on a Mueller Matrix if and a
Sample
Systematic Errors
Vacuum
Vacuum (four-zone averaging:
Isotropic
Isotropic (four-zone averaging:
Anisotropic dielectric S
Anisotropic dielectric S (four-zone averaging:
Errors for all optical elements have been simulated between to (step ) with and without four-zone averaging method. Three samples are studied: vacuum, isotropic , and anisotropic dielectric S [13]. The results are presented as mean error ± its standard deviation.
Tables (5)
Table 1
Second-Order Errors Due to Azimuthal Mispositioning of Element
Error
Special Configuration
Without
Without
Four-zone averaging:
Four-zone averaging:
Table 2
Calculated Elements of Matrix [Eq. (17)] for the First Compensatora
Coefficient
Value
The functions and are null if a two-zone measurement in A is performed independently of the angle . is defined in Eq. (18).
Table 3
Calculated Elements of Matrix [Eq. (17)] for the Second Compensatora
Coefficient
Value
The functions and are null if a two-zone measurement in P is performed independently of the angle . is defined in Eq. (18).
Table 4
Systematic Errors in Mueller Matrix Ellipsometer for Isotropic Sample if and when the Four-Zone Averaging Measurement Method is Performed
Origin
Table 5
Statistical Study of the Influence of Element Mispositioning on a Mueller Matrix if and a
Sample
Systematic Errors
Vacuum
Vacuum (four-zone averaging:
Isotropic
Isotropic (four-zone averaging:
Anisotropic dielectric S
Anisotropic dielectric S (four-zone averaging:
Errors for all optical elements have been simulated between to (step ) with and without four-zone averaging method. Three samples are studied: vacuum, isotropic , and anisotropic dielectric S [13]. The results are presented as mean error ± its standard deviation.